/usr/share/doc/libghc-lazysmallcheck-dev/examples/Countdown.hs is in libghc-lazysmallcheck-dev 0.6-9.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 | module Countdown where
-----------------------------------------------------------------------------
--
-- The Countdown Problem
--
-- Graham Hutton
-- University of Nottingham
--
-- November 2001
--
-----------------------------------------------------------------------------
-----------------------------------------------------------------------------
-- Formally specifying the problem
-----------------------------------------------------------------------------
data Op = Add | Sub | Mul | Div
deriving Eq
valid :: Op -> Int -> Int -> Bool
valid Add _ _ = True
valid Sub x y = x > y
valid Mul _ _ = True
valid Div x y = x `mod` y == 0
apply :: Op -> Int -> Int -> Int
apply Add x y = x + y
apply Sub x y = x - y
apply Mul x y = x * y
apply Div x y = x `div` y
data Expr = Val Int | App Op Expr Expr
deriving Eq
values :: Expr -> [Int]
values (Val n) = [n]
values (App _ l r) = values l ++ values r
eval :: Expr -> [Int]
eval (Val n) = [n | n > 0]
eval (App o l r) = [apply o x y | x <- eval l, y <- eval r, valid o x y]
subbags :: [a] -> [[a]]
subbags xs = [zs | ys <- subs xs, zs <- perms ys]
subs :: [a] -> [[a]]
subs [] = [[]]
subs (x:xs) = ys ++ map (x:) ys
where
ys = subs xs
perms :: [a] -> [[a]]
perms [] = [[]]
perms (x:xs) = concat (map (interleave x) (perms xs))
interleave :: a -> [a] -> [[a]]
interleave x [] = [[x]]
interleave x (y:ys) = (x:y:ys) : map (y:) (interleave x ys)
solution :: Expr -> [Int] -> Int -> Bool
solution e ns n = elem (values e) (subbags ns) && eval e == [n]
-----------------------------------------------------------------------------
-- Brute force implementation
-----------------------------------------------------------------------------
split :: [a] -> [([a],[a])]
split [] = [([],[])]
split (x:xs) = ([],x:xs) : [(x:ls,rs) | (ls,rs) <- split xs]
nesplit :: [a] -> [([a],[a])]
nesplit = filter ne . split
ne :: ([a],[b]) -> Bool
ne (xs,ys) = not (null xs || null ys)
exprs :: [Int] -> [Expr]
exprs [] = []
exprs [n] = [Val n]
exprs ns = [e | (ls,rs) <- nesplit ns
, l <- exprs ls
, r <- exprs rs
, e <- combine l r]
combine :: Expr -> Expr -> [Expr]
combine l r = [App o l r | o <- ops]
ops :: [Op]
ops = [Add,Sub,Mul,Div]
solutions :: [Int] -> Int -> [Expr]
solutions ns n = [e | ns' <- subbags ns, e <- exprs ns', eval e == [n]]
-----------------------------------------------------------------------------
-- Fusing generation and evaluation
-----------------------------------------------------------------------------
type Result = (Expr,Int)
results :: [Int] -> [Result]
results [] = []
results [n] = [(Val n,n) | n > 0]
results ns = [res | (ls,rs) <- nesplit ns
, lx <- results ls
, ry <- results rs
, res <- combine' lx ry]
combine' :: Result -> Result -> [Result]
combine' (l,x) (r,y) = [(App o l r, apply o x y) | o <- ops, valid o x y]
solutions' :: [Int] -> Int -> [Expr]
solutions' ns n = [e | ns' <- subbags ns, (e,m) <- results ns', m == n]
-----------------------------------------------------------------------------
-- Exploiting arithmetic properties
-----------------------------------------------------------------------------
valid' :: Op -> Int -> Int -> Bool
valid' Add x y = x <= y
valid' Sub x y = x > y
valid' Mul x y = x /= 1 && y /= 1 && x <= y
valid' Div x y = y /= 1 && x `mod` y == 0
eval' :: Expr -> [Int]
eval' (Val n) = [n | n > 0]
eval' (App o l r) = [apply o x y | x <- eval' l, y <- eval' r, valid' o x y]
solution' :: Expr -> [Int] -> Int -> Bool
solution' e ns n = elem (values e) (subbags ns) && eval' e == [n]
results' :: [Int] -> [Result]
results' [] = []
results' [n] = [(Val n,n) | n > 0]
results' ns = [res | (ls,rs) <- nesplit ns
, lx <- results' ls
, ry <- results' rs
, res <- combine'' lx ry]
combine'' :: Result -> Result -> [Result]
combine'' (l,x) (r,y) = [(App o l r, apply o x y) | o <- ops, valid' o x y]
solutions'' :: [Int] -> Int -> [Expr]
solutions'' ns n = [e | ns' <- subbags ns, (e,m) <- results' ns', m == n]
-----------------------------------------------------------------------------
-- Interactive version for testing
-----------------------------------------------------------------------------
instance Show Op where
show Add = "+"
show Sub = "-"
show Mul = "*"
show Div = "/"
instance Show Expr where
show (Val n) = show n
show (App o l r) = bracket l ++ show o ++ bracket r
where
bracket (Val n) = show n
bracket e = "(" ++ show e ++ ")"
display :: [Expr] -> IO ()
display [] = putStr "\nThere are no solutions.\n\n"
display (e:es) = do putStr "\nOne possible solution is "
putStr (show e)
putStr ".\n\nPress return to continue searching..."
getLine
putStr "\n"
if null es then
putStr "There are no more solutions.\n\n"
else
do sequence [print e | e <- es]
putStr "\nThere were "
putStr (show (length (e:es)))
putStr " solutions in total.\n\n"
-- Properties
infixr 0 -->
False --> _ = True
True --> x = x
prop_lemma1 :: ([Int], [Int], [Int]) -> Bool
prop_lemma1 (xs, ys, zs) = ((xs,ys) `elem` split zs) == (xs ++ ys == zs)
prop_lemma3 :: ([Int], [Int], [Int]) -> Bool
prop_lemma3 (xs, ys, zs) = ((xs, ys) `elem` nesplit zs)
== (xs ++ ys == zs && ne (xs, ys))
prop_lemma4 :: ([Int], [Int], [Int]) -> Bool
prop_lemma4 (xs, ys, zs) = ((xs, ys) `elem` nesplit zs) -->
(length xs < length zs && length ys < length zs)
prop_solutions (ns, m) = solutions ns m == solutions' ns m
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